In image processing, statistical calculation, such as average value calculation, is applied in some cases to a subject region when the barycenter of the subject is calculated. For example, in palm vein authentication, image processing apparatuses that execute palm vein authentication calculate a mean average value of coordinates of each point in a palm of a hand being a subject, to identify the barycenter (Japanese Laid-open Patent Publication Nos. 2009-238205 and 2007-233981).
However, there has been a problem that it is difficult to achieve statistical calculation for a subject region accurately when the subject of image processing is inclined. For example, taking the palm vein authentication as an example, the problem that it is difficult to achieve statistical calculation accurately when an image of a subject region to be an authentication feature is processed is explained.
FIG. 11 explains influence caused when a subject is inclined. As depicted in FIG. 11, a camera projects a subject on an imaging device. When the subject is inclined, imaged areas of the subject to be projected in one pixel of the imaging device are not uniform. That is, a region B of the subject projected in a pixel PB has a larger image area than a region A of the subject projected in a pixel PA. In other words, in the pixel PB, the region B that is longer than the region A is projected. The data amount of the pixel PB is underestimated compared to the data amount of the pixel PA.
In such a case, for example, the image processing apparatus calculates barycentric coordinates XG by using following Equation (1). N refers to the total number of pixels, and xi refers to coordinates of i-th pixel. That is, in barycenter calculation, all pixels are calculated with the uniform weight of 1.0.
                              X          G                =                              ∑                          i              =              1                        N                    ⁢                                    x              i                        /            N                                              (        1        )            
This results in underestimation of the data amount of the region B compared to the data amount of the region A. Inversely, the data amount of the region A is overestimated compared to the data amount of the region A. As a result, the barycentric coordinates XG are drawn toward the direction of the region A, to be miscalculated.
The above problem is not limited only to the case of the subject being inclined, but also applies to the case of the subject being bent.